OpenSCAD inside/outside diameter of polygons

thingiverse

When crafting items, we often face the challenge of fitting unusual shapes into standard spaces. Specifically, how tiny does a square peg need to be to slide smoothly into a round hole? Conversely, what size must a round hole become to accommodate a square peg comfortably? These questions arise frequently when designing innovative products, which is why I've compiled some mathematical formulas for your reference in this library.